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Quantitative Methods

Quantitative Methods. Model Selection I: principles of model choice and designed experiments. Model Selection I: principles of model choice. The problem of model choice. Model Selection I: principles of model choice. The problem of model choice. Model Selection I: principles of model choice.

scott-rush
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Quantitative Methods

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  1. Quantitative Methods Model Selection I: principles of model choice and designed experiments

  2. Model Selection I: principles of model choice The problem of model choice

  3. Model Selection I: principles of model choice The problem of model choice

  4. Model Selection I: principles of model choice The problem of model choice Varying b Varying a Y = a + bX

  5. Model Selection I: principles of model choice The problem of model choice Varying c Y = a + bX + cX2

  6. Model Selection I: principles of model choice The problem of model choice Varying d, Part II Varying d, Part I Varying c Y = a + bX + cX2 Y = a + bX + cX2 + dX3 Any continuous curve can be sufficiently well approximately by a polynomial of high enough order.

  7. Model Selection I: principles of model choice The problem of model choice Y1 = -7.62 + 3.189*X1 + 0.825*X12

  8. Model Selection I: principles of model choice The problem of model choice Y1 = -15.75 + 6.179*X1 + 0.6169*X12 + 0.00500*X13

  9. Model Selection I: principles of model choice The problem of model choice Linear Quadratic Cubic … Y1 = X1 Y1 = X1|X1 Y1 = X1|X1|X1 … Y1 = -128.08 + 29.473*X1 Y1 = -7.62 + 3.189*X1 + 0.825*X12 Y1 = -15.75 + 6.179*X1 + 0.6169*X12 + 0.00500*X13 …

  10. Model Selection I: principles of model choice Principles of model choice

  11. Model Selection I: principles of model choice Principles of model choice • Economy of variables • Multiplicity of p-values • Marginality

  12. Model Selection I: principles of model choice Principles of model choice • Economy of variables • Multiplicity of p-values • Marginality • Hierarchies must be respected in model formulae • Significance of interactions includes importance of main effects • Do not test main effects with a SS that has been adjusted for the interaction

  13. Model Selection I: principles of model choice Principles of model choice What does marginal mean? A is marginal to A*B, A*B*C, A*X*X A is not marginal to B, B*C, B*C*X X is marginal to X*X, A*X, A*B*X X is not marginal to A, Z, Z*Z, A*B, A*B*Z

  14. Model Selection I: principles of model choice Principles of model choice Why marginal?

  15. Model Selection I: principles of model choice Principles of model choice • Economy of variables • Multiplicity of p-values • Marginality • Hierarchies must be respected in model formulae • Significance of interactions includes importance of main effects • Do not test main effects with a SS that has been adjusted for the interaction

  16. Model Selection I: principles of model choice Principles of model choice Y=X Y=X+X*X Y=X+X*X+X*X*X Hierarchical Y=X*X Y=X*X + X Y=X*X*X + X Not hierarchical Lower order term missing Lower order term after higher order term Lower order term missing and wrong order

  17. Model Selection I: principles of model choice Principles of model choice • Economy of variables • Multiplicity of p-values • Marginality • Hierarchies must be respected in model formulae • Significance of interactions includes importance of main effects • Do not test main effects with a SS that has been adjusted for the interaction

  18. Y B=1 B=2 1 2 3 A Model Selection I: principles of model choice Principles of model choice No main effect of A because the average value of Y at each level of A is the same. No main effect of B because the average value of Y at each level of B is the same. Yet there is an interaction, and this means A and B both affect Y.

  19. Y B=1 B=2 1 2 3 A Model Selection I: principles of model choice Principles of model choice No main effect of A because the average value of Y at each level of A is the same. No main effect of B because the average value of Y at each level of B is the same. Yet there is an interaction, and this means A and B both affect Y. (i) a significant interaction A*B means that A affects the way B affects Y, (ii) but then certainly B must affect Y. So if A*B is significant, conclude that A and B affect Y as well as the direct inference that A affects the way B affects Y.

  20. Model Selection I: principles of model choice Principles of model choice • Economy of variables • Multiplicity of p-values • Marginality • Hierarchies must be respected in model formulae • Significance of interactions includes importance of main effects • Do not test main effects with a SS that has been adjusted for the interaction

  21. Model Selection I: principles of model choice Principles of model choice

  22. Model Selection I: principles of model choice Principles of model choice

  23. Model Selection I: principles of model choice Principles of model choice

  24. Model Selection I: principles of model choice Principles of model choice

  25. Model Selection I: principles of model choice Choosing a model

  26. Model Selection I: principles of model choice Choosing a model: polynomials

  27. Model Selection I: principles of model choice Choosing a model: polynomials

  28. Model Selection I: principles of model choice Choosing a model: polynomials Y1 = -7.62 + 3.189*X1 + 0.825*X12 s = square-root(6010) = 77.52

  29. Model Selection I: principles of model choice Choosing a model: orthogonal design

  30. Model Selection I: principles of model choice Choosing a model: orthogonal design bottom up! pooling?

  31. Model Selection I: principles of model choice Choosing a model: non-orthogonality

  32. Model Selection I: principles of model choice Choosing a model: non-orthogonality

  33. Model Selection I: principles of model choice Choosing a model: non-orthogonality

  34. Model Selection I: principles of model choice Choosing a model: trends in a factor - Shape - Sensitivity to consistent effects

  35. Model Selection I: principles of model choice Choosing a model: trends in a factor

  36. Model Selection I: principles of model choice Choosing a model: trends in a factor

  37. Model Selection I: principles of model choice Choosing a model: trends in a factor

  38. Model Selection I: principles of model choice Choosing a model: trends in a factor Sensitivity

  39. Model Selection I: principles of model choice Choosing a model: trends in a factor Shape

  40. Model Selection I: principles of model choice Last words… • Model choice represents a whole extra layer of sophistication to use of GLM • Very powerful extensions: polynomials • Very important principles: economy, multiplicity • Very important cautions: marginality Model Selection II: datasets with several explanatory variables Read Chapter 11

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